New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-05
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Construction of higher-order optimal and globally convergent methods for computing simple roots of nonlinear equations is an earliest and challenging problem in numerical analysis.
Therefore, the aim of this paper is to present optimal and globally convergent families of King's method and Ostrowski's method having biquadratic and eight-order convergence, respectively, permitting f′(x)=0 in the vicinity of the required root.
Fourth-order King's family and Ostrowski's method can be seen as special cases of our proposed scheme.
All the methods considered here are found to be more effective to the similar robust methods available in the literature.
In their dynamical study, it has been observed that the proposed methods have equal or better stability and robustness as compared to the other methods.
American Psychological Association (APA)
Behl, Ramandeep& Kanwar, Vinay. 2014. New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0. International Journal of Mathematics and Mathematical Sciences،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-458653
Modern Language Association (MLA)
Behl, Ramandeep& Kanwar, Vinay. New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0. International Journal of Mathematics and Mathematical Sciences No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-458653
American Medical Association (AMA)
Behl, Ramandeep& Kanwar, Vinay. New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting f′(xn)=0. International Journal of Mathematics and Mathematical Sciences. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-458653
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-458653